Atrial fibrillation (AF) is the most common arrhythmia encountered in clinical practice, occurring in 1% of the adult population of North America. Although AF does not typically lead to risk of immediate mortality, it is a potent risk factor for ischemic stroke. When left untreated AF reduces quality of life, functional status, cardiac performance and is associated with higher medical costs and an increased risk of death. Catheter ablation is a commonly used treatment method for those who suffer from drugrefractory AF. Prior to ablation, intra-cardiac mapping can be used to determine the activation sequence of cardiac tissue, which may be useful in deciding where to place ablation lesions. However, the electrical potential that is recorded during mapping is not a direct reflection of the current density across the tissue because the potential recorded at each point above the heart tissue is influenced by every cell in the tissue. This causes the recorded potential to be a blurred version of the true tissue current density. The potential that is observed can be described as the convolution of the true current density with a point spread function. Accordingly, deconvolution can, in principle, be used in order to improve the resolution of potential maps. However, because the number of electrodes which can be deployed transvenously is limited by practical restrictions, the recorded potential field is a sparsely sampled version of the actual potential field. Further, an electrode array cannot sample over the entire atrial surface, so the potential map that is observed is a truncated version of the global electrical activity. Here, we investigate the effects of electrode sampling density and edge extension on the ability of deconvolution to improve the resolution of measured electrical potentials within the atria of the heart. In particular, we identify the density of sensing electrodes that are required to allow deconvolution to provide improved estimation of the true current density when compared to the observed potential field.